Coherent three parameter rows
ProvedD1Bound5.coherent_three_parameter_rowsdiophantine-tuplesnumber-theory
All exact rational comparisons for the manuscript's two rows.
Preamble
import Mathlib.Algebra.BigOperators.NatAntidiagonal import Mathlib.Algebra.QuadraticAlgebra.Basic import Mathlib.Algebra.Ring.Basic import Mathlib.Algebra.Ring.Equiv import Mathlib.Analysis.Analytic.Binomial import Mathlib.Analysis.Complex.Basic import Mathlib.Analysis.Complex.Norm import Mathlib.Analysis.Normed.Ring.Basic import Mathlib.Analysis.SpecificLimits.Normed import Mathlib.Data.Fin.VecNotation import Mathlib.Data.Finset.Card import Mathlib.Data.Finset.Insert import Mathlib.Data.Int.GCD import Mathlib.Data.Sym.Basic import Mathlib.Data.Sym.Card import Mathlib.LinearAlgebra.Dimension.Free import Mathlib.LinearAlgebra.Lagrange import Mathlib.NumberTheory.NumberField.InfinitePlace.TotallyRealComplex import Mathlib.NumberTheory.NumberField.Norm import Mathlib.RingTheory.Binomial import Mathlib.RingTheory.MvPolynomial.Symmetric.Defs import Mathlib.Tactic.Linarith import Mathlib.Tactic.LinearCombination import Definitions.Def_D1Bound5_CoherentThreeParameters_Definitions
Formal statement
section
open Finset
noncomputable section
namespace D1Bound5
theorem _root_.D1Bound5.coherent_three_parameter_rows :
(0 < coherentThreeLowerConstant 32 ∧
100*coherentThreeUpperConstant 32/99 < (1/10 : ℝ) ∧
5 < 100/(201*coherentThreeUpperConstant 32) ∧
100/(199*coherentThreeLowerConstant 32) < 179/10) ∧
(0 < coherentThreeLowerConstant 48 ∧
100*coherentThreeUpperConstant 48/99 < (19/200 : ℝ) ∧
5 < 100/(201*coherentThreeUpperConstant 48) ∧
100/(199*coherentThreeLowerConstant 48) < 15) := by sorry
end D1Bound5
end
Source
D1Bound5/CoherentThreeParameters.lean, lines 152-162, SHA-256 ca0fac013bc4ef76939f023e46143eabcee36be640a6d47b13f0373264757949. Project: https://github.com/tomislav-math/d1-bound5-lean